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Calc 1 5.3

 

<== Calculus 1
Number Question Answer
See the work
1. Evaluate the integral

integral from 0 to 0.9 dx/sqrt(1-x^2})

1.12
The work

Point Cost: 1
2. Evaluate the integral

integral from 1 to sqrt(4) 4/(1+x^2) dx

4.429
The work

Point Cost: 1
3. Evalute the definite integral.

integral from  0 to pi/8 sec(x)tan(x) dx

Integral =
0.08239
The work

Point Cost: 1
4. Evaluate the definite integral

integral from 3 to 6 (2x + 8) dx
51
The work

Point Cost: 1
5. Evaluate the definite integral

integral from  2 to 9 (3 x^2 -8 x + 8) dx
469
The work

Point Cost: 1
6. Evaluate the definite integral:

integral from 8 to 14 dx =

6
The work

Point Cost: 1
7. Evaluate the definite integral:

integral from 3 to 25 6sqrt(x)dx} =

479.21
The work

Point Cost: 1
8. Evaluate the definite integral:

integral from -7 to -4 (-3 x^(-2) + x^(-1))dx} =

-0.88104
The work

Point Cost: 2
9. Evaluate the definite integral:

integral from -2 to 2 (6 x - e^x)dx} =

-7.2537
The work

Point Cost: 1
10. Evaluate the definite integral

integral from  0 to pi 8sin(x) dx
16
The work

Point Cost: 1
11. Evaluate the definite integral:

integral from 2 to -2 (x-1)(7 x + 6)dx} =

-40/3
The work

Point Cost: 2
12. Evaluate the definite integral:

ntegral from  0 to 4 sqrt(r)+1/sqrt(r)dr} =

28/3
The work

Point Cost: 2
13. Evaluate integral from 3 to 4 1/ x^2 dx.

Answer:
1/12
The work

Point Cost: 1
14. Evaluate the definite integral

integral from 2 to 6  3/sqrt(x)dx

6.212
The work

Point Cost: 1
15. integral from 2 to 5 (3 x^2 + 1)/(x^2)dx = 9.3
The work

Point Cost: 2
16. Evaluate the definite integral

integral from 1 to 6 (10 x^2 + 5)/sqrt(x)dx
363.22
The work

Point Cost: 2
17. integral from 3 to 5 (x^(4) + 3)/(x) dx = 137.53
The work

Point Cost: 2
18. integral from 0 to 4 u^(5)(sqrt(u)+(u)^(1/3) du = 2286.938
The work

Point Cost: 1
19. Evaluate the definite integral

integral from 0.8 to 1.4  6sec^2(x) dx
28.609
The work

Point Cost: 1
20. integral from 0 to 1 (2 e^x+4 sin x) dx = 5.275
The work

Point Cost: 1
21. Evaluate the definite integral:

integral from 3 to 4 (t^(13) - t^(5))/t^(9) dt =

156.1928
The work

Point Cost: 2
22. Evaluate the definite integral.

integral from 3 to 7 5^t dt
48464.12
The work

Point Cost: 1
23. Evaluate the definite integral.

integral from 4 to 9 (5+ xsqrt(x)) dx
109.4
The work

Point Cost: 1
24. integral from 0 to pi/4 (3 + cos^3(u))/(cos^2 u) du = 3.707
The work

Point Cost: 3
25. integral from 1 to e (5 x^2 + 7 x +6)/(x)dx} = 34
The work

Point Cost: 1
26. Evaluate the definite integral:

integral from -8 to 8 (x - 6 abs(x)) dx} =

-384
The work

Point Cost: 3
27. Consider the function

f(x) = \left\lbrace\begin{array}{ll}x &\mbox{if\ } x<1\ rac{1}{x} &\mbox{if\ } x\ge 1nd{array}
ight.
Evaluate the definite integral.
integral from -3 to 7 f(x)dx
-2.054
The work

Point Cost: 3
28. Evaluate integral from 0 to 2 f(x) dx}, where

f(x) = \begin{cases}
        3 x^{9}, & 0 \leq x < 1 \
        4 x^{2}, & 1 \leq x \leq 2.
        nd{cases}


integral from 0 to 2 f(x) dx} =
289/30
The work

Point Cost: 3
29. Evaluate integral from -pi to pi f(x) dx}, where

f(x) = \begin{cases}
        6 x^{4}, & -\pi \leq x < 0 \
        7 \sin(x), & 0 \leq x \leq \pi.
        nd{cases}


integral from -pi to pi f(x) dx =
381.22
The work

Point Cost: 3
30. Evaluate the indefinite integral:

integral 8 dx} = + C.

8x
The work

Point Cost: 0
31. Evaluate the indefinite integral:

integral 8 e^t dt} = + C.

integral 8 e^t dt} = 8 e^t
The work

Point Cost: 0
32. Evaluate the indefinite integral:

integral (6 x^2 + 3 x - 3) dx} = + C.

integral(6 x^2 + 3 x - 3) dx} =
The work

Point Cost: 1
33. Evaluate the indefinite integral:

integral (e^x - 5 x)/(4) dx} = + C.

integral (e^x - 5 x)/(4) dx} =
The work

Point Cost: 1
34. Evaluate the indefinite integral:

integral (5 z^(-3) + 7 z^(-2) + 4 z^(-1) dz) = + C.

integral (5 z^(-3) + 7 z^(-2) + 4 z^(-1) dz)  =
The work

Point Cost: 1
35. Evaluate the indefinite integral:

integral (5)/x^(1/3)) - 4 x^(2/3) dx = + C.

integral (5)/x^(1/3)) - 4 x^(2/3) dx =
The work

Point Cost: 2
36. Evaluate the indefinite integral:

integral (5 x^4 - 5 x)/(x^3) dx} = + C.

integral (5 x^4 - 5 x)/(x^3) dx} =
The work

Point Cost: 1
37. Evaluate the indefinite integral:

integral (8 - 7xe^x)/(x) dx} = + C.

integral(8 - 7xe^x)/(x)dx} =
The work

Point Cost: 1
38. Compute the indefinite integral.

integral (1-sin^2x)/(cos x) dx
+ C
sin(x)
The work

Point Cost: 3
39. Find a particular function which is an indefinite integral for:

integral (5 x + sec(x)tan(x)) dx

integral (5 x + sec(x)tan(x)) dx
The work

Point Cost: 1
40. Evaluate the indefinite integral:

integral (6 x^4 - 6/x^(4) - 3) dx = + C.

integral (6 x^4 - 6/x^(4) - 3) dx =
The work

Point Cost: 2
41. Evaluate the indefinite integral:

integral x(5 + 5 x^(6)) dx} = + C.

integral x(5 + 5 x^(6)) dx} =
The work

Point Cost: 1
42. Evaluate the indefinite integral:

integral (x^(5) + 5 + (5)/(x^(2)+1) dx} = + C.

integral (x^(5) + 5 + (5)/(x^(2)+1) dx} =
The work

Point Cost: 3
43. Evaluate the indefinite integral:

integral (7 e^(u) + 5 sec^2u) du} = + C.

integral (7 e^(u) + 5 sec^2u) du} =
The work

Point Cost: 1
44. Evaluate the indefinite integral:

integral 3sin(2x)/(8sinx) dx} = + C.

0.75*sin(x)
The work

Point Cost: 3
45. The velocity function is v(t) =  t^2 - 4 t + 3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,6].

displacement =

distance traveled =

displacement = 104/3

distance traveled = 112/3

The work

Point Cost: 4
46. The linear density of a rod of length 4 m is given by

rho(x) = 5 + 10sqrt(x)
measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the rod.

Total mass =

Total mass = 220/3
The work

Point Cost: 3
47. A population of cattle is increasing at a rate of 400 + 30t per year, where t is measured in years. By how much does the population increase between the 4 th and the 9 th years.

Total Increase =

Total Increase = 2975
The work

Point Cost: 3